Sombor index and eigenvalues of weakly zero-divisor graph of commutative rings
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| Format: | Preprint |
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2025
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| _version_ | 1866908335938207744 |
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| author | Shariq, Mohd Kumar, Jitender |
| author_facet | Shariq, Mohd Kumar, Jitender |
| contents | The weakly zero-divisor graph $WΓ(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two distinct vertices $x$, $y$ are adjacent if and only if there exist $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, we determine the Sombor index for the weakly zero-divisor graph of the integers modulo ring $\mathbb{Z}_n$. Furthermore, we investigate the Sombor spectrum and establish bounds for the Sombor energy of the weakly zero-divisor graph of $\mathbb{Z}_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sombor index and eigenvalues of weakly zero-divisor graph of commutative rings Shariq, Mohd Kumar, Jitender Combinatorics Rings and Algebras Spectral Theory 05C25, 05C50 The weakly zero-divisor graph $WΓ(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two distinct vertices $x$, $y$ are adjacent if and only if there exist $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, we determine the Sombor index for the weakly zero-divisor graph of the integers modulo ring $\mathbb{Z}_n$. Furthermore, we investigate the Sombor spectrum and establish bounds for the Sombor energy of the weakly zero-divisor graph of $\mathbb{Z}_n$. |
| title | Sombor index and eigenvalues of weakly zero-divisor graph of commutative rings |
| topic | Combinatorics Rings and Algebras Spectral Theory 05C25, 05C50 |
| url | https://arxiv.org/abs/2504.17265 |